What I didn't point out is that their word for water is « i » - which makes one wonder whether the similarity with our own word (see etymology for island, or watery land) is purely coincidental, or pehaps there is some hitherto obscure relationship between these two language families.

of course, the coincidence (if that is indeed what it is) does bring to mind notions of neural pathways and the hard wiring that apparently dictates much of what we do, perhaps even the sound of our languages.

It may seem hard to believe, but Latin aqua, “water,” is related to island, which originally meant “watery land.” Aqua comes almost unchanged from Indo-European *akw?-, “water.” *Akw?- became *ahw?- in Germanic by Grimm's Law and other sound changes. To this was built the adjective *ahwj?–, “watery.” This then evolved to *awwj?– or *auwi–, which in pre-English became *?aj–, and finally ?g or ?eg in Old English. Island, spelled iland, first appears in Old English in King Alfred's translation of Boethius about A.D. 888; the spellings igland and ealond appear in contemporary documents. The s in island is due to a mistaken etymology, confusing the etymologically correct English iland with French isle. Isle comes ultimately from Latin ?nsula “island,” a component of paen?nsula, “almost-island,” whence our peninsula.

-- the Houghton Mifflin Dictionary

I'm not aware of how far back the Straits of Behring were supposed to have served as the bridge for reaching the American continent but if the PIE was «akwa», I'm not sure that Guarani could be related since by the time «akwa» made its way into the « i » sound in Europe (3-5th centura AD), the Guarani were already in America.

still it's coincidental isn't it? perhaps the Guarani started out with «akwa» too and followed a similar trajectory to the current sound?

Maybe I could remind you that the name France comes from Franks a German tribe (comp. Frankfurt in Germany). I have a theory that the French language is a bastard language made up of vulgar Latin taken over by invading Germanic nations and molded with Germanic grammar and a sprinkling of vocablary which made that basically Roman language more palateble to Germanic speaking peoples and therefore became easier to digest and hence "popular" in the Abend länder.
Is that -ing ?

More seriously, I don't think French is to be considered a mongrel language. Taking English as an example of a truly mongrel tongue, we see that huge amounts of vocabulary came in from Old Norman to join the already caothic Anglo-Saxon mixture. Three tongues contributing their full linguistic luggage, which they placed upon the Briton's ground so that you could spot some Celtic terms here and there. Do you think you can compare that with the Franks being diluted into the enormously greater Latin-speaking population? Franks, who, by the bye, were already latinised through the limes. We mustn't forget that Latin exercised its influence beyond the boundaries of the Empire.

On the other hand, what would you say of Spanish and Portuguese, whose vocabulary (I extrapolate from the Spanish data I've got) is made up to a 20% of Arabic words? Furthermore, the Visigoths, like the Franks in the Gaul, also conquered the whole of Hispania, but again they, extremely latinised as they were, brought us little more than war terms (witness of what they came to do).